If you're not already aware of it,
Marc Chauvin has an excellent winter Presi Traverse guide on his site. Pretty much everything you need to know. He even includes the vectors and coords of the escape routes (which you should have several waterproof copies of distributed among your party).
I did it in 1975 in a party of 5 (4 is the recommended minimum), so lightweight, warm gear didn't really exist (this was before polyester fleece was available), esp. on a college student's budget. Our packs were around 65 - 70 lbs. We planned for 3-4 nights out, going north to south, up the Airline trail and out over Webster to Crawford Notch. We took food for 8 days, and, because of being pinned down by two storms, did it in 7 days. We spent 36 hrs in the (no longer there) Edmunds Col shelter. Winds on Washington hit 150mph during that storm. Because of yet another storm approaching, we bypassed staying at Lake of the Clouds hut and went from Edmunds Col to Mizpah Springs hut in one long, grueling day. We went over every summit.
One other tip: if you haven't done a lot of hiking wearing crampons, make sure you practice...before you lacerate one of your legs a day or more from help. Practice with snowshoes as well if you lack the skills, especially going up steep terrain. Step kicking with snowshoes is a learned skill. Assuming a normal winter, you will hike many miles in both crampons and snowshoes. Also, know how to self arrest - you will cross several snowfields where, if firm, a fall and slide could have very unpleasant consequences. Some of these have avi potential as well, so know the warning signs, triggers, and safe travel protocol.
You might want to rethink March if possible - it's the month with the greatest number of days of winds over 100mph. Contrary to popular belief, you cannot hike (and make reasonable progress) in much more than 55mph winds. Also, people tend to seriously overestimate wind speed. So when someone tells you about the time they hiked Washington in 75mph winds, you can safely assume it was actually blowing at about 40mph.
Make sure you understand food requirements. It actually gets difficult to eat the number of calories/day needed to stay warm and fuel the amount of physical labor. 5000 cal/day is not an unusual requirement.